Math Problem Statement
f h(x) is the inverse of f(x), what is the value of h(f(x))
Solution
If is the inverse of , then by the definition of inverse functions, applying to returns the original input . In mathematical terms, this can be written as:
This is because the function maps to some value, and the inverse function undoes that mapping, bringing it back to .
Would you like more details on inverse functions, or do you have any questions?
Here are 5 related questions to expand on this:
- What is the formal definition of an inverse function?
- How do you find the inverse of a function algebraically?
- What is the graphical relationship between a function and its inverse?
- Can all functions have inverses? Why or why not?
- What happens if is not one-to-one? Can it still have an inverse?
Tip: A function must be one-to-one (injective) in order to have an inverse function.
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Function Composition
Formulas
h(f(x)) = x, where h(x) is the inverse of f(x)
Theorems
Inverse Function Theorem
Suitable Grade Level
Grades 9-12